C₁₁×#32874 #14610067

order	2816
nilpotency class	3
isoclinism	isoclinic class of #32873
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₁×#32874

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#2840
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
prime radical	C₂²×C₁₁×#41	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂⁴×C₁₁ ◁ G

688 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,26)(16,20)(17,21)(18,25)(19,28)(23,32)(24,35)(27,40)(29,34)(30,37)(31,39)(33,41)(36,43)(38,42);(12,14)(13,18,21,22)(15,23)(16,24)(17,25)(19,32,26,30)(20,31,34,35)(27,38)(28,37)(29,39)(33,42,40,43)(36,41);(12,15)(13,19,21,26)(14,23)(16,27)(17,28)(18,30,22,32)(20,33,34,40)(24,38)(25,37)(29,41)(31,43,35,42)(36,39);(12,16,17,29)(13,20,21,34)(14,24,25,39)(15,27,28,41)(18,31,22,35)(19,33,26,40)(23,36,37,38)(30,42,32,43)

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 25862);